Solution :
Given that ,
mean = = 30
standard deviation = = 4
P(30< x < 35) = P[(30-30) / 4< (x - ) / < (35-30) / 4)]
= P(0 < Z <1.25 )
= P(Z < 1.25) - P(Z < 0)
Using z table
= 0.8944-0.5000
=0.3944
b.
P(x > 21) = 1 - P(x< 21)
= 1 - P[(x -) / < (21-30) /4 ]
= 1 - P(z < -2.25)
Using z table
= 1 - 0.0122
= 0.9878
c.
P(X< 40) = P[(X- ) / < (40-30) / 4]
= P(z <2.5 )
Using z table
= 0.9938
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